CHATTANOOGA, Tenn., July 16 (Reuters) - Investigators on Thursday sought to determine what led a 24-year-old gunman to open fire at two military offices in Chattanooga, Tennessee, killing four Marines in an attack officials said could be an act of domestic terrorism.

Mohammod Youssuf Abdulazeez, identified as the shooter by the Federal Bureau of Investigation, was shot to death in the rampage that also injured three people.

The attack comes at a time when U.S. military and law enforcement authorities are increasingly concerned about the threat posed by "lone wolves" to domestic targets.

NBC News reported that Abdulazeez was a naturalized American who was born in Kuwait. U.S. law enforcement officials said they were investigating whether he was inspired by Islamic State or a similar group.

Islamic State had threatened to step up violence in the holy fasting month of Ramadan, which ends on Friday evening.

The extremist group, also known as ISIS and ISIL, claimed responsibility when a gunman in Tunisia opened fire at a popular tourist hotel and killed 37 people in June. On the same day, there was an attack in France and a suicide bombing in Kuwait.

The SITE Intelligence Group, which tracks extremist groups, said that Abdulazeez blogged on Monday that "life is short and bitter" and Muslims should not miss an opportunity to "submit to Allah." Reuters could not independently verify the blog postings.

Police officers enter the Armed Forces Career Center through a bullet-riddled door after a gunman opened fire on the building Thursday, July 16, 2015, in Chattanooga, Tenn. Authorities say there were multiple casualties including the gunman.

The New York Times, citing unnamed law enforcement officials, reported that his father had been under investigation several years ago over possible ties to a foreign terrorist organization and had been on a terrorist watch list.

The father was later removed from that list and the investigation did not reveal any information about his son, the Times said.

The Tennessean newspaper reported that two women were taken away in handcuffs from Abdulazeez's home on Thursday evening. Reuters could not immediately confirm that report.

According to a resume believed to have been posted online by Abdulazeez, he attended high school in a Chattanooga suburb and graduated from the University of Tennessee with an engineering degree.

"I remember him being very creative. He was a very light minded kind of individual. All his videos were always very unique and entertaining," said Greg Raymond, 28, who worked with Abdulazeez on a high school television program.

"He was a really calm, smart and cool person who joked around. Like me he wasn't very popular so we always kind of got along. He seemed like a really normal guy," Raymond said.

Mary Winter, president of the Colonial Shores Neighborhood Association, said she had known Abdulazeez and his family for more than 10 years and was stunned at the crime.

"We're all shocked and saddened," Winter said. "He never caused any trouble. We can't believe that this happened. We were just planning to have a swim team banquet tonight."

President Barack Obama offered his condolences to the victims' families and said officials will be prompt and thorough in getting answers on the shootings.

"It is a heartbreaking circumstance for these individuals who have served our country with great valor to be killed in this fashion," he said in a statement from the Oval Office.

The Department of Homeland Security was stepping up security at certain federal facilities and supporting the FBI investigation, DHS Secretary Jeh Johnson said in a statement.

Chattanooga is a city of about 173,000 people along the Tennessee River in the southeast of the state.

The suspect, seen driving an open-top Ford Mustang, first went to a joint military recruiting center in a strip mall and sprayed it with gunfire, riddling the glass facade with bullet holes.

"Everybody was at a standstill and as soon as he pulled away everyone scrambled trying to make sure everyone was OK," said Erica Wright, who works two doors down from the center.

Armed forces recruiting centers are often located in shopping centers and other prominent places.

The gunman then drove off to a Naval Reserve Center about 6 miles (10 km) away, fatally shooting the four Marines before being shot and killed in a firefight with police.

Three others were wounded in the attacks, including a police officer reported in stable condition and a Marine.

The shootings began at about 10:45 a.m. local time (1445 GMT) and ended about 30 minutes later.

At least three people were wounded in the attacks, including a Marine and a Navy sailor who is in critical condition, according to the hospital. One of those hurt was a police officer who was in stable condition.

Police blocked access to the street where the suspected gunman lived in an upscale suburb.

Local media said memorial services for the victims would be held in various Chattanooga churches tonight.

"We condemn this horrific attack in the strongest terms possible," said Nihad Awad, national director of the Council on American-Islamic Relations.

There have been other attacks on U.S. military personnel in the United States.

In 2009, former U.S. Army major Nidal Hasan fatally shot 13 people at Fort Hood in Texas. He said he targeted unarmed soldiers preparing for deployment in retaliation for U.S. wars in the Muslim world.

And in May, two gunmen opened fire with assault rifles at a heavily guarded Texas exhibit of caricatures of the Prophet Mohammad. Both men were shot to death by responding authorities.

(Reporting by Suzannah Gonzales in Chicago, Eric Johnson in Seattle, Brendan O'Brien in Milwaukee, David Bailey in Minneapolis, Frank McGurty and Katie Reiley in New York, Emily Stephenson, Julia Edwards, Lindsay Dunsmuir, Doina Chiacu and David Alexander in Washington and Dan Whitcomb in Los Angeles; Writing by Jon Herskovitz and Dan Whitcomb; Editing by Jonathan Oatis, James Dalgleish and Lisa Shumaker)